#include <TriangulateBourke.h>
//The original C version is ritten by P. Bourke. See http://paulbourke.net/papers/triangulate/.
//The C++ version is written by Gilles Dumoulin.
#include <algorithm>

namespace TriangulateBourke
{
	namespace _Internal
	{
		const double EPSILON = 1.0e-12; //0.000001;

		////////////////////////////////////////////////////////////////////////
		// CircumCircle() :
		//   Return true if a point (xp,yp) is inside the circumcircle made up
		//   of the points (x1,y1), (x2,y2), (x3,y3)
		//   The circumcircle centre is returned in (xc,yc) and the radius r
		//   Note : A point on the edge is inside the circumcircle
		////////////////////////////////////////////////////////////////////////

		int CircumCircle(double xp, double yp, double x1, double y1, double x2, 
			double y2, double x3, double y3, double &xc, double &yc, double &r){
				double m1, m2, mx1, mx2, my1, my2;
				double dx, dy, rsqr, drsqr;

				/* Check for coincident points */
				if(abs(y1 - y2) < EPSILON && abs(y2 - y3) < EPSILON)
					return(false);
				if(abs(y2-y1) < EPSILON){ 
					m2 = - (x3 - x2) / (y3 - y2);
					mx2 = (x2 + x3) / 2.0;
					my2 = (y2 + y3) / 2.0;
					xc = (x2 + x1) / 2.0;
					yc = m2 * (xc - mx2) + my2;
				}else if(abs(y3 - y2) < EPSILON){ 
					m1 = - (x2 - x1) / (y2 - y1);
					mx1 = (x1 + x2) / 2.0;
					my1 = (y1 + y2) / 2.0;
					xc = (x3 + x2) / 2.0;
					yc = m1 * (xc - mx1) + my1;
				}else{
					m1 = - (x2 - x1) / (y2 - y1); 
					m2 = - (x3 - x2) / (y3 - y2); 
					mx1 = (x1 + x2) / 2.0; 
					mx2 = (x2 + x3) / 2.0;
					my1 = (y1 + y2) / 2.0;
					my2 = (y2 + y3) / 2.0;
					xc = (m1 * mx1 - m2 * mx2 + my2 - my1) / (m1 - m2); 
					yc = m1 * (xc - mx1) + my1; 
				}
				dx = x2 - xc;
				dy = y2 - yc;
				rsqr = dx * dx + dy * dy;
				r = sqrt(rsqr); 
				dx = xp - xc;
				dy = yp - yc;
				drsqr = dx * dx + dy * dy;
				return((drsqr <= rsqr) ? true : false);
		}
		///////////////////////////////////////////////////////////////////////////////
		// Triangulate() :
		//   Triangulation subroutine
		//   Takes as input NV vertices in array pxyz
		//   Returned is a list of ntri triangular faces in the array v
		//   These triangles are arranged in a consistent clockwise order.
		//   The triangle array 'v' should be malloced to 3 * nv
		//   The vertex array pxyz must be big enough to hold 3 more points
		//   The vertex array must be sorted in increasing x values say
		//
		//   qsort(p,nv,sizeof(XYZ),XYZCompare);
		///////////////////////////////////////////////////////////////////////////////

		int Triangulate(int nv, XYZ pxyz[], ITRIANGLE v[], int &ntri){
			int *complete = NULL;
			IEDGE *edges = NULL; 
			IEDGE *p_EdgeTemp;
			int nedge = 0;
			int trimax, emax = 200;
			int status = 0;
			int inside;
			int i, j, k;
			double xp, yp, x1, y1, x2, y2, x3, y3, xc, yc, r;
			double xmin, xmax, ymin, ymax, xmid, ymid;
			double dx, dy, dmax; 

			/* Allocate memory for the completeness list, flag for each triangle */
			trimax = 4 * nv;
			complete = new int[trimax];
			/* Allocate memory for the edge list */
			edges = new IEDGE[emax];
			/*
			Find the maximum and minimum vertex bounds.
			This is to allow calculation of the bounding triangle
			*/
			xmin = pxyz[0].x;
			ymin = pxyz[0].y;
			xmax = xmin;
			ymax = ymin;
			for(i = 1; i < nv; i++){
				if (pxyz[i].x < xmin) xmin = pxyz[i].x;
				if (pxyz[i].x > xmax) xmax = pxyz[i].x;
				if (pxyz[i].y < ymin) ymin = pxyz[i].y;
				if (pxyz[i].y > ymax) ymax = pxyz[i].y;
			}
			dx = xmax - xmin;
			dy = ymax - ymin;
			dmax = (dx > dy) ? dx : dy;
			xmid = (xmax + xmin) / 2.0;
			ymid = (ymax + ymin) / 2.0;
			/*
			Set up the supertriangle
			his is a triangle which encompasses all the sample points.
			The supertriangle coordinates are added to the end of the
			vertex list. The supertriangle is the first triangle in
			the triangle list.
			*/
			pxyz[nv+0].x = xmid - 20 * dmax;
			pxyz[nv+0].y = ymid - dmax;
			pxyz[nv+1].x = xmid;
			pxyz[nv+1].y = ymid + 20 * dmax;
			pxyz[nv+2].x = xmid + 20 * dmax;
			pxyz[nv+2].y = ymid - dmax;
			v[0].p1 = nv;
			v[0].p2 = nv+1;
			v[0].p3 = nv+2;
			complete[0] = false;
			ntri = 1;
			/*
			Include each point one at a time into the existing mesh
			*/
			for(i = 0; i < nv; i++){
				xp = pxyz[i].x;
				yp = pxyz[i].y;
				nedge = 0;
				/*
				Set up the edge buffer.
				If the point (xp,yp) lies inside the circumcircle then the
				three edges of that triangle are added to the edge buffer
				and that triangle is removed.
				*/
				for(j = 0; j < ntri; j++){
					if(complete[j])
						continue;
					x1 = pxyz[v[j].p1].x;
					y1 = pxyz[v[j].p1].y;
					x2 = pxyz[v[j].p2].x;
					y2 = pxyz[v[j].p2].y;
					x3 = pxyz[v[j].p3].x;
					y3 = pxyz[v[j].p3].y;
					inside = CircumCircle(xp, yp, x1, y1, x2, y2, x3, y3, xc, yc, r);
					if (xc + r < xp)
						// Suggested
						//if (xc + r + EPSILON < xp)
							complete[j] = true;
					if(inside){
						/* Check that we haven't exceeded the edge list size */
						if(nedge + 3 >= emax){
							emax += 100;
							p_EdgeTemp = new IEDGE[emax];
							for (int i = 0; i < nedge; i++) { // Fix by John Bowman
								p_EdgeTemp[i] = edges[i];   
							}
							delete []edges;
							edges = p_EdgeTemp;
						}
						edges[nedge+0].p1 = v[j].p1;
						edges[nedge+0].p2 = v[j].p2;
						edges[nedge+1].p1 = v[j].p2;
						edges[nedge+1].p2 = v[j].p3;
						edges[nedge+2].p1 = v[j].p3;
						edges[nedge+2].p2 = v[j].p1;
						nedge += 3;
						v[j] = v[ntri-1];
						complete[j] = complete[ntri-1];
						ntri--;
						j--;
					}
				}
				/*
				Tag multiple edges
				Note: if all triangles are specified anticlockwise then all
				interior edges are opposite pointing in direction.
				*/
				for(j = 0; j < nedge - 1; j++){
					for(k = j + 1; k < nedge; k++){
						if((edges[j].p1 == edges[k].p2) && (edges[j].p2 == edges[k].p1)){
							edges[j].p1 = -1;
							edges[j].p2 = -1;
							edges[k].p1 = -1;
							edges[k].p2 = -1;
						}
						/* Shouldn't need the following, see note above */
						if((edges[j].p1 == edges[k].p1) && (edges[j].p2 == edges[k].p2)){
							edges[j].p1 = -1;
							edges[j].p2 = -1;
							edges[k].p1 = -1;
							edges[k].p2 = -1;
						}
					}
				}
				/*
				Form new triangles for the current point
				Skipping over any tagged edges.
				All edges are arranged in clockwise order.
				*/
				for(j = 0; j < nedge; j++) {
					if(edges[j].p1 < 0 || edges[j].p2 < 0)
						continue;
					v[ntri].p1 = edges[j].p1;
					v[ntri].p2 = edges[j].p2;
					v[ntri].p3 = i;
					complete[ntri] = false;
					ntri++;
				}
			}
			/*
			Remove triangles with supertriangle vertices
			These are triangles which have a vertex number greater than nv
			*/
			for(i = 0; i < ntri; i++) {
				if(v[i].p1 >= nv || v[i].p2 >= nv || v[i].p3 >= nv) {
					v[i] = v[ntri-1];
					ntri--;
					i--;
				}
			}
			delete[] edges;
			delete[] complete;
			return 0;
		} 

		int XYZCompare(const void *v1, const void *v2){
			XYZ *p1, *p2;

			p1 = (XYZ*)v1;
			p2 = (XYZ*)v2;
			if(p1->x < p2->x)
				return(-1);
			else if(p1->x > p2->x)
				return(1);
			else
				return(0);
		}
	}

	std::vector<Triplet> DelaunayTriangulation(const std::vector<CParticleF>& points)
	{
		int nv = points.size() + 3;
		_Internal::XYZ* pxyz = new _Internal::XYZ[nv];
		for(int i=0; i<points.size(); ++i)
		{
			pxyz[i].x = (double)points[i].m_X;
			pxyz[i].y = (double)points[i].m_Y;
			pxyz[i].z = 0;
		}
		pxyz[nv-1].x = 0;
		pxyz[nv-1].y = 0;
		pxyz[nv-1].z = 0;

		_Internal::ITRIANGLE* v = new _Internal::ITRIANGLE[3*nv];
		qsort(pxyz, points.size(), sizeof(_Internal::XYZ), _Internal::XYZCompare);
		int ntri;
		Triangulate(points.size(),pxyz,v,ntri);

		std::vector<Triplet> triangles(ntri);
		for(int i=0; i<ntri; ++i)
		{
			//revert it back to the pre-sorted order
			int k1 = std::distance(points.begin(), std::find(points.begin(), points.end(), CParticleF(pxyz[v[i].p1].x, pxyz[v[i].p1].y, pxyz[v[i].p1].z)));
			triangles[i].index[0] = k1;
			int k2 = std::distance(points.begin(), std::find(points.begin(), points.end(), CParticleF(pxyz[v[i].p2].x, pxyz[v[i].p2].y, pxyz[v[i].p2].z)));
			triangles[i].index[1] = k2;
			int k3 = std::distance(points.begin(), std::find(points.begin(), points.end(), CParticleF(pxyz[v[i].p3].x, pxyz[v[i].p3].y, pxyz[v[i].p3].z)));
			triangles[i].index[2] = k3;
		}
		delete [] pxyz;
		delete [] v;
		return triangles;
	}
}
